de-Broglie Hypothesis and it’s Derivation

According to phenomena like reflection,refraction,interference, light is wave nature.but according to phenomena like black body radiation, Photoelectric effect ,light radiation is particles nature. so,light exhibits both characters i.e. wave nature and particle nature.

de-broglie hypothesis

This two nature is first analysed by de-broglie and gave a hypothesis. This hypothesis is called de-broglie hypotgesis.

According to de-broglie’s, the wavelength of matter(particles) is moving in a space is equal to the ratio of value of planck’s constant and linear momentum of the matter.

so, λ = h/p

or,

,where h= planck’s constant

m = mass of matter

v = velocity of matter

Derivation of de-Broglie’s Hypothesis

Let us consider a photon of frequency of moving with speed ‘c’and its energy is

E = hf …….1)

According to Einestein mass energy equivalent to matter is,

E = mc2 …….2)

From equation 1 and 2,

hf = mc2

hf/λ = mc. c

hc/λ = p.c

h/λ = p

λ = h/mv [where p = mv]

It is the required expression of de-broglie hypothesis.

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